A293078 a(n) = (1/2)*A293077(n).

1, 2, 3, 5, 8, 13, 22, 37, 63, 107, 182, 310, 529, 903, 1541, 2630, 4489, 7663, 13081, 22330, 38119, 65073, 111086, 189635, 323727, 552636, 943408, 1610498, 2749292, 4693335, 8012024, 13677380, 23348748, 39858806, 68043238

Offset: 1

Author

Clark Kimberling, Sep 30 2017

Keywords

• nonn
• easy

Crossrefs

Cf. A289035, A293076, A293077.

Programs

Mathematica

z = 10; (* number of iterations *)
s = {0, 0}; u[0] = StringJoin[Map[ToString, s]]; w[0] = u[0];
u[n_] := u[n] = StringReplace[w[n - 1], {"00" -> "0010", "01" -> "010", "10" -> "010"}];
w[n_] := w[n] = If[OddQ[StringLength[u[n]]], StringDrop[u[n], -1], u[n]];
TableForm[Table[w[n], {n, 0, 8}]]
st = ToCharacterCode[w[z]] - 48  (* A293076 *)
p0 = Flatten[Position[st, 0]] (* A289036 *)
p1 = Flatten[Position[st, 1]]  (* A289037 *)
v = Table[StringLength[w[n]], {n, 0, 34}] (* A293077 *)
v/2  (* A293078 *)